性质（u）在序列空间cesp（En）中的提升

主要研究了性质（u）从Banach空间En到序列空间cesp（En）的提升问题．     

性质(u)在置换空间P_XX_n上的提升

主要讨论性质 ( u)从 Banach空间 Xn 到 PXXn 的提升问题 ,它是 lp( Xn)中相应结果的推广 .     

I(L)弱诱导空间

引入 I(L)弱诱导空间与 I(L)底空间的概念 ,证明 I(L )弱诱导空间是遗传的、可乘的 ,给出一个 I(L)拓扑空间是 I(L )弱诱导空间的充分必要条件。     

中国各地区PM_(2.5)影响因素的空间差异特征分析

基于空间变系数模型,采用局部线性BGWR拟合方法,分别从经济、人口和环境的角度,选取9个指标,对2016年中国各地区PM_(2.5)浓度的空间差异性及其影响因素进行探究.结果表明:降水、天气、森林覆盖率、对外开放水平、污染治理和地区生产总值与PM_(2.5)浓度显著负相关;单位GDP能耗、产业结构和城镇化率与PM_(2.5)浓度显著正相关.其中,天气因素和城镇化率的影响程度较其他因素更为显著.最后,提出人口空间合理布局、产业结构优化升级等建议,旨在成功实现PM_(2.5)污染控制和减排.     

(IC)式Stone-(C)ech紧化

以Hutton单位区间I(L)的外(IC)化空间(L)作为标准单位区间,引入了相应的(IC)完全正则分离性,建立了这类空间的嵌入理论并给出了(IC)式Stone-(C)ech紧化定理.     

欧氏空间中子流形的曲率与几何性质

研究了欧氏空间En p中具常数量曲率n(n-1)r的n(n>2)维完备连通子流形,得到了En p截面曲率非负且法联络平坦的完备连通子流形的一个分类定理.     

关于(C-K)性质和L-KR空间的对偶性质

证明了(C-K)性质,(S-K)性质,L-KR空间,L-KS空间和CL-KR空间和CL-KS空间的一些充要条件.这些条件表明了(C-K)与(S-K)性质,L-KR与L-KS空间及CL-KR空间与CL-KS空间之间的对偶性质.     

H~(Ba)(D)空间的内插定理(英文)

研究了一类由 Hp空间构成的 Ba空间的内插性质 ,给出了 HBa(D)空间的三个内插定理     

Lbaa(D)空间的内插性质

研究了一类由Bergman空间Lpa(D)构成的Ba空间的内插性质,给出了Lbaa(D)空间的三个内插定理.     

在空间W_0~(1，x)L~(P(x))(Q)及其共轭空间中的若干收敛性定理

本文证明了在空间W_0~(1,x)L~(p(x))(Q)及其共轭空间中三个收敛性定理.在附加较弱条件的情况下,给出了几乎处处收敛蕴含弱收敛,弱收敛蕴含强收敛.     

Curve selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G, each connected component of the set E_n(G)of all elements of order n in G is a conjugacy class in G. In particular, all conjugacy classes of finite order in G are closed. Some properties of connected components of E_n(G) are also given.     

On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation

In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E_n(F,β) where E_n(F,β) is the error in approximating of the function F(s) by definite integral polynomials in the half plane Res≤βα.     

A New Type of Euler Polynomials and Numbers

By defining two specific exponential generating functions, we introduce a kind of Euler polynomials and study its basic properties in detail. As an application of the introduced polynomials, we use them in computing some new series of Taylor type that contain the associated Euler numbers \(E_n(0)\) where \(E_n(x)\) is the Euler polynomial.     

DEGREE OF COPOSITIVE POLYNOMIAL APPROXIMATION

Denoteby _n(f) the degree of copositive approximation to f(x) by polynomials of degree≤n. For function f(x) ∈ C~k[-1, 1] which alternates in sign finitely many timesin [-1, 1], the author obtains the following Jackson type estimates_n(f)≤Cn~(-k)w(f~(k), 1/n)foa any positive integer k.     

On the growth and approximation of entire functions represented by Laplace–Stieltjes’ transformation

In the present paper, we obtain the characterization of various growth parameters of an entire function F(s) represented by Laplace–Stieltjes transformation in terms of the rate of decrease of \(E_n ( {F,\beta } ),\)where \(E_n ( {F,\beta } )\) represents the error in approximating the function F(s) by exponential polynomials.     

Asymptotic Behavior of Factorization and Projection Constants

This paper is concerned with estimates of important factorization constants that appear in Banach space theory. We prove upper bounds of the Hilbertian norm of projections on finite-dimensional spaces of interpolation spaces generated by certain abstract interpolation functors and show applications to Calderón–Lozanovskii spaces. We also prove estimates of the p-factorization norm and projection constants for finite-dimensional Banach lattices. We show as a consequence of our results that in a large class of n-dimensional Banach sequence lattices \(E_n\) the projection constants \(\lambda (E_n)\) satisfy \(\lim _{n\rightarrow \infty }\lambda (E_n)/\sqrt{n} = c\), where \(c=\sqrt{2/\pi }\) in the real case and \(c= \sqrt{\pi }/2\) in the complex case. Applications are given to vector-valued sequence spaces.     

Multiple commutator formulas

Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I _i , i = 0, …,m, be two-sided ideals of A, GL _n (A, I _i ) be the principal congruence subgroup of level I _i in GL _n (A) and E _n (A, I _i ) be the relative elementary subgroup of level I _i . We prove the multiple commutator formula $$\left[ {{E_n}(A,{I_0}),{\rm{G}}{{\rm{L}}_n}(A,{I_1}),{\rm{G}}{{\rm{L}}_n}(A,{I_2}), \ldots ,{\rm{G}}{{\rm{L}}_n}(A,{I_m})} \right] = \left[ {{E_n}(A,{I_0}),{E_n}(A,{I_1}),{E_n}(A,{I_2}), \ldots ,{E_n}(A,{I_m})} \right],$$ , which is a broad generalization of the standard commutator formulas. This result contains all the published results on commutator formulas over commutative rings and answers a problem posed by A. Stepanov and N. Vavilov.     

静电场理论中微分几何方法的一个应用

引用微分几何的方法导出了静电场中曲面导体表面附近场强的法向分量的法向变化率与曲面两个主曲率的关系式,并作为特例,导出了静电场理论的一个众所周知的经典公式.     

A sharp constant in the Jackson-Stechkin inequality in the space L2 on the period

In the space L ² of real-valued measurable 2π-periodic functions that are square summable on the period [0, 2π], the Jackson-Stechkin inequality

SOME CONVERSE RESULTS ON ONESIDED APPROXIMATION ： JUSTIFICATIONS

The present paper deals with best onesided approximation rate in Lp spaces ^~En（f）Lp of f∈C2π.Although it is clear that the estimate ^~E(f)Lp≤C‖f‖Lp cannot be correct for all f∈L^p2π in case p＜∞, the question whether ~En(f)Lp≤Cω(f,n^-l)Lp or ^~En(f)Lp≤CEn(f)Lp holds for f∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.